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These sample problems below for Trinomial Factoring were generated by the MathScore.com engine.

Sample Problems For Trinomial Factoring

Complexity=1, Mode=simple

Factor the expression as completely as possible.
1.   x 2 - 2x - 3
2.   x 2 + 6x - 7

Complexity=3, Mode=prefix

Factor the expression as completely as possible.
1.   6x 2 - 90x + 156
2.   - 3x 3 - 21x 2 + 54x

Complexity=4, Mode=frontConst

Factor the expression as completely as possible.
1.   4x 2 - 18x - 70
2.   - 6x 3 - 105x 2 - 186x

Complexity=5, Mode=includeY

Factor the expression as completely as possible.
1.   5x 3 + 38x 2y + 69xy 2
2.   12x 3 + 196x 2y + 392xy 2

Complexity=6, Mode=hardest

Factor the expression as completely as possible.
1.   - 8w 2x 2z 2 - 176wxyz - 246y 2
2.   - 2w 3x 12z 3 + 14w 2x 8yz 2 - 20wx 4y 2z

Answers

Complexity=1, Mode=simple

Factor the expression as completely as possible.
#ProblemCorrect AnswerYour Answer
1x 2 - 2x - 3
Solution
Front coefficient is 1. Factors are: 1
Back coefficient is -3. Factors are: 1, 3
Now test combinations of these factors to get the middle value of - 2x.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to - 2x.
Test: (x + 1)(x - 3) => - 3x + x = - 2x This combination matches.
Result: x 2 + - 2x + - 3

#ProblemCorrect AnswerYour Answer
2x 2 + 6x - 7
Solution
Front coefficient is 1. Factors are: 1
Back coefficient is -7. Factors are: 1, 7
Now test combinations of these factors to get the middle value of 6x.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to 6x.
Test: (x + 1)(x - 7) => - 7x + x = - 6x
Test: (x + 7)(x - 1) => -x + 7x = 6x This combination matches.
Result: x 2 + 6x + - 7

Complexity=3, Mode=prefix

Factor the expression as completely as possible.
#ProblemCorrect AnswerYour Answer
16x 2 - 90x + 156
Solution
Factor out 6 from 6x 2 + - 90x + 156
6(x 2 - 15x + 26)
Front coefficient is 1. Factors are: 1
Back coefficient is 26. Factors are: 1, 2, 13, 26
Now test combinations of these factors to get the middle value of - 15x.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to - 15x.
Test: (x - 1)(x - 26) => - 26x + -x = - 27x
Test: (x - 2)(x - 13) => - 13x + - 2x = - 15x This combination matches.
Result: 6x 2 + - 90x + 156

#ProblemCorrect AnswerYour Answer
2- 3x 3 - 21x 2 + 54x
Solution
Factor out - 3x from - 3x 3 + - 21x 2 + 54x
- 3x(x 2 + 7x - 18)
Front coefficient is 1. Factors are: 1
Back coefficient is -18. Factors are: 1, 2, 3, 6, 9, 18
Now test combinations of these factors to get the middle value of 7x.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to 7x.
Test: (x + 1)(x - 18) => - 18x + x = - 17x
Test: (x + 2)(x - 9) => - 9x + 2x = - 7x
Test: (x + 3)(x - 6) => - 6x + 3x = - 3x
Test: (x + 6)(x - 3) => - 3x + 6x = 3x
Test: (x + 9)(x - 2) => - 2x + 9x = 7x This combination matches.
Result: - 3x 3 + - 21x 2 + 54x

Complexity=4, Mode=frontConst

Factor the expression as completely as possible.
#ProblemCorrect AnswerYour Answer
14x 2 - 18x - 70
Solution
Factor out 2 from 4x 2 + - 18x + - 70
2(2x 2 - 9x - 35)
Front coefficient is 2. Factors are: 1, 2
Back coefficient is -35. Factors are: 1, 5, 7, 35
Now test combinations of these factors to get the middle value of - 9x.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to - 9x.
Test: (x + 1)(2x - 35) => - 35x + 2x = - 33x
Test: (x + 5)(2x - 7) => - 7x + 10x = 3x
Test: (x + 7)(2x - 5) => - 5x + 14x = 9x
Test: (x + 35)(2x - 1) => -x + 70x = 69x
Test: (x - 1)(2x + 35) => 35x + - 2x = 33x
Test: (x - 5)(2x + 7) => 7x + - 10x = - 3x
Test: (x - 7)(2x + 5) => 5x + - 14x = - 9x This combination matches.
Result: 4x 2 + - 18x + - 70

#ProblemCorrect AnswerYour Answer
2- 6x 3 - 105x 2 - 186x
Solution
Factor out - 3x from - 6x 3 + - 105x 2 + - 186x
- 3x(2x 2 + 35x + 62)
Front coefficient is 2. Factors are: 1, 2
Back coefficient is 62. Factors are: 1, 2, 31, 62
Now test combinations of these factors to get the middle value of 35x.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to 35x.
Test: (x + 1)(2x + 62) => 62x + 2x = 64x
Test: (x + 2)(2x + 31) => 31x + 4x = 35x This combination matches.
Result: - 6x 3 + - 105x 2 + - 186x

Complexity=5, Mode=includeY

Factor the expression as completely as possible.
#ProblemCorrect AnswerYour Answer
15x 3 + 38x 2y + 69xy 2
Solution
Factor out x from 5x 3 + 38x 2y + 69xy 2
x(5x 2 + 38xy + 69y 2)
Front coefficient is 5. Factors are: 1, 5
Back coefficient is 69. Factors are: 1, 3, 23, 69
Now test combinations of these factors to get the middle value of 38xy.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to 38xy.
Test: (x + y)(5x + 69y) => 69xy + 5xy = 74xy
Test: (x + 3y)(5x + 23y) => 23xy + 15xy = 38xy This combination matches.
Result: 5x 3 + 38x 2y + 69xy 2

#ProblemCorrect AnswerYour Answer
212x 3 + 196x 2y + 392xy 2
Solution
Factor out 4x from 12x 3 + 196x 2y + 392xy 2
4x(3x 2 + 49xy + 98y 2)
Front coefficient is 3. Factors are: 1, 3
Back coefficient is 98. Factors are: 1, 2, 7, 14, 49, 98
Now test combinations of these factors to get the middle value of 49xy.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to 49xy.
Test: (x + y)(3x + 98y) => 98xy + 3xy = 101xy
Test: (x + 2y)(3x + 49y) => 49xy + 6xy = 55xy
Test: (x + 7y)(3x + 14y) => 14xy + 21xy = 35xy
Test: (x + 14y)(3x + 7y) => 7xy + 42xy = 49xy This combination matches.
Result: 12x 3 + 196x 2y + 392xy 2

Complexity=6, Mode=hardest

Factor the expression as completely as possible.
#ProblemCorrect AnswerYour Answer
1- 8w 2x 2z 2 - 176wxyz - 246y 2
Solution
Factor out - 2 from - 8w 2x 2z 2 + - 176wxyz + - 246y 2
- 2(4w 2x 2z 2 + 88wxyz + 123y 2)
Front coefficient is 4. Factors are: 1, 2, 4
Back coefficient is 123. Factors are: 1, 3, 41, 123
Now test combinations of these factors to get the middle value of 88wxyz.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to 88wxyz.
Test: (wxz + y)(4wxz + 123y) => 123wxyz + 4wxyz = 127wxyz
Test: (wxz + 3y)(4wxz + 41y) => 41wxyz + 12wxyz = 53wxyz
Test: (wxz + 41y)(4wxz + 3y) => 3wxyz + 164wxyz = 167wxyz
Test: (wxz + 123y)(4wxz + y) => wxyz + 492wxyz = 493wxyz
Test: (2wxz + y)(2wxz + 123y) => 246wxyz + 2wxyz = 248wxyz
Test: (2wxz + 3y)(2wxz + 41y) => 82wxyz + 6wxyz = 88wxyz This combination matches.
Result: - 8w 2x 2z 2 + - 176wxyz + - 246y 2

#ProblemCorrect AnswerYour Answer
2- 2w 3x 12z 3 + 14w 2x 8yz 2 - 20wx 4y 2z
Solution
Factor out - 2wx 4z from - 2w 3x 12z 3 + 14w 2x 8yz 2 + - 20wx 4y 2z
- 2wx 4z(w 2x 8z 2 - 7wx 4yz + 10y 2)
Front coefficient is 1. Factors are: 1
Back coefficient is 10. Factors are: 1, 2, 5, 10
Now test combinations of these factors to get the middle value of - 7wx 4yz.

For each test, do a partial FOIL. Multiply the outer factors and inner factors and add them together to see if they are equal to - 7wx 4yz.
Test: (wx 4z - y)(wx 4z - 10y) => - 10wx 4yz + -wx 4yz = - 11wx 4yz
Test: (wx 4z - 2y)(wx 4z - 5y) => - 5wx 4yz + - 2wx 4yz = - 7wx 4yz This combination matches.
Result: - 2w 3x 12z 3 + 14w 2x 8yz 2 + - 20wx 4y 2z

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